A and B can do piece of work in 12 days; B and C in 15 days; C and A in 20 days. In how many days will they finish it together and separately ?

Explanation

`A` and `B` can do a piece of work in `12` days
In day both can do
`A+B=1/12` part of the work ........(i)
`B` and `C` can do the work in `15` days
Therefore in `1` day both can do
`B+C=1/15` part............(ii)
`C` and `A` can do the same work in `20` days
In `1` days both can do
`A+C=1/20` part..............(iii)
Adding `2(A+B+C)=1/12+1/15+1/20`
Adding all , we get
`2(A+B+C)=(5+4+3)/60`
`2(A+B+C)=12/60`
`2(A+B+C)=1/5`
`(A+B+C)= 1/10` work
C completes work `= (A+B+C)-(A+B)`
`=1/10-1/12`
C completes the whole work in 60 days
Similarly,
`B+C=1/15`
`B+(1/60)=1/15`
`B= 1/15-1/60`
`B=1/20`
B completes work in 20 days
` A+B=1/12`
` A+1/20=1/12`
`A= 1/12-1/20`
`A= 1/30`
A completes work in 30 days.